Singular measures in circle dynamics

Critical circle homeomorphisms have an invariant measure totally singular with respect to the Lebesgue measure. We prove that singularities of the invariant measure are of Holder type. The Hausdorff dimension of the invariant measure is less than 1 but greater than 0

Giant Shapiro steps for two-dimensional Josephson-junction arrays with time-dependent Ginzburg-Landau dynamics

Two-dimensional Josephson junction arrays at zero temperature are investigated numerically within the resistively shunted junction (RSJ) model and the time-dependent Ginzburg-Landau (TDGL) model with global conservation of current implemented through the fluctuating twist boundary condition (FTBC). Fractional giant Shapiro steps are found for {\em both} the RSJ and TDGL cases. This implies that the local current conservation, on which the RSJ model is based, can be relaxed to the TDGL dynamics with only global current conservation, without changing the sequence of Shapiro steps. However, when the maximum widths of the steps are compared for the two models some qualitative differences are found at higher frequencies. The critical current is also calculated and comparisons with earlier results are made. It is found that the FTBC is a more adequate boundary condition than the conventional uniform current injection method because it minimizes the influence of the boundary.Comment: 6 pages including 4 figures in two columns, final versio

Structural Relaxation, Self Diffusion and Kinetic Heterogeneity in the Two Dimensional Lattice Coulomb Gas

We present Monte Carlo simulation results on the equilibrium relaxation dynamics in the two dimensional lattice Coulomb gas, where finite fraction $f$ of the lattice sites are occupied by positive charges. In the case of high order rational values of $f$ close to the irrational number $1-g$ ($g\equiv(\sqrt{5} -1)/2$ is the golden mean), we find that the system exhibits, for wide range of temperatures above the first-order transition, a glassy behavior resembling the primary relaxation of supercooled liquids. Single particle diffusion and structural relaxation show that there exists a breakdown of proportionality between the time scale of diffusion and that of structural relaxation analogous to the violation of the Stokes-Einstein relation in supercooled liquids. Suitably defined dynamic cooperativity is calculated to exhibit the characteristic nature of dynamic heterogeneity present in the system.Comment: 12 pages, 20 figure

CFT description of the Fully Frustrated XY model and phase diagram analysis

Following a suggestion given in Nucl. Phys. B 300 (1988)611,we show how the U(1)*Z_{2} symmetry of the fully frustrated XY (FFXY) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at "paired states" fillings nu =1 (cfr. Cristofano et al.,Mod. Phys. Lett. A 15 (2000)1679;Nucl. Phys. B 641 (2002)547). The resulting twisted conformal field theory (CFT) with central charge c=2 is shown to well describe the physical properties of the FFXY model. In particular the whole phase diagram is recovered by analyzing the flow from the Z_{2} degenerate vacuum of the c=2 CFT to the infrared fixed point unique vacuum of the c=3/2 CFT. The last theory is known to successfully describe the critical behavior of the system at the overlap temperature for the Ising and vortex-unbinding transitions.Comment: 18 pages, 1 figure, to appear in JSTA

Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant

Intertrade duration of equities is an important financial measure characterizing the trading activities, which is defined as the waiting time between successive trades of an equity. Using the ultrahigh-frequency data of a liquid Chinese stock and its associated warrant, we perform a comparative investigation of the statistical properties of their intertrade duration time series. The distributions of the two equities can be better described by the shifted power-law form than the Weibull and their scaled distributions do not collapse onto a single curve. Although the intertrade durations of the two equities have very different magnitude, their intraday patterns exhibit very similar shapes. Both detrended fluctuation analysis (DFA) and detrending moving average analysis (DMA) show that the 1-min intertrade duration time series of the two equities are strongly correlated. In addition, both multifractal detrended fluctuation analysis (MFDFA) and multifractal detrending moving average analysis (MFDMA) unveil that the 1-min intertrade durations possess multifractal nature. However, the difference between the two singularity spectra of the two equities obtained from the MFDMA is much smaller than that from the MFDFA.Comment: 10 latex pages, 4 figure

Directed Polymers with Random Interaction : An Exactly Solvable Case -

We propose a model for two $(d+1)$-dimensional directed polymers subjected to a mutual $\delta$-function interaction with a random coupling constant, and present an exact renormalization group study for this system. The exact $\beta$-function, evaluated through an $\epsilon(=1-d)$ expansion for second and third moments of the partition function, exhibits the marginal relevance of the disorder at $d=1$, and the presence of a phase transition from a weak to strong disorder regime for $d>1$. The lengthscale exponent for the critical point is $\nu=1/2\mid\epsilon\mid$. We give details of the renormalization. We show that higher moments do not require any new interaction, and hence the $\beta$ function remains the same for all moments. The method is extended to multicritical systems involving an $m$ chain interaction. The corresponding disorder induced phase transition for $d>d_m=1/(m-1)$ has the critical exponent ${\nu}_m=[2d(m-1)-2]^{-1}$. For both the cases, an essential singularity appears for the lengthscale right at the upper critical dimension $d_m$. We also discuss the strange behavior of an annealed system with more than two chains with pairwise random interactions among each other.Comment: No of pages: 36, 7figures on request, Revtex3, Report No:IP/BBSR/929

Beyond the periodic orbit theory

The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory approach to determining eigenspectra of transfer operators.Comment: 29 pages Latex2